Fourier Transform Mass Spectrometry (FTMS) uses an electromagnetic field in which coherent packets of ions undergo free harmonic oscillations within the analyser with a period that is a function of their mass to charge (m/z) ratio. The electromagnetic field can be provided by the combination of an electrostatic field and a magnetostatic field, for example in a Fourier Transform Ion Cyclotron Resonance (FTICR) mass analyser, or by an electrostatic field only, for example in an orbital trapping mass analyser (marketed under the name Orbitrap™). FTMS using RF fields are also known, but did not become widespread due to limited analytical performance.
Typically, ions are detected by an image current generated in detection electrodes as the ions pass nearby. It is known that the resolving power of m/z analysis in FTMS is limited by the Fourier Transform uncertainty principle. This rigidly links the resolving power to the number of detected coherent oscillations of ion packets. As a result, increasing the detection time in an FTMS mass analyser results in a proportional improvement of resolving power of m/z analysis.
Frequently, liquid separation is performed before mass analysis and the increasing speed of such separation is putting pressure on the detection time in mass spectrometry and tandem mass spectrometry analysis. Reducing detection time without significantly affecting resolving power is a major challenge in FTMS.
Existing approaches deal with data processing of the harmonic transient image current, also termed a continuous transient image current, that is generated when the detection time is at least the length of the ion packet oscillation period. For example, the following approaches have been considered: auto-correlation (see Marshall A. G.; Verdun, F. R., “Fourier Transforms in NMR, optical and mass spectrometry”, Elsevier, 1990, p. 150-155); Linear Prediction (see Guan S., Marshall A. G., “Linear Prediction Cholesky Decomposition vs Fourier Transform Spectral Analysis for Ion Cyclotron Resonance Mass Spectrometry”, Anal. Chem., 1997, 69 (6), pp 1156-1162 and U.S. Pat. No. 5,047,636); and Filter Diagonalization Method (FDM) (see Mandelshtam, V. A., “FDM: The filter diagonalization method for data processing in NMR experiments”, Prog. Nucl. Magn. Res. Spectrosc., 2001, 38, p. 159-196).
These existing approaches attempt to fit the harmonic transient, which is a time-domain signal, to a sum of sinusoids or cosinusoids. This is known as the harmonic inversion problem and is a difficult non-linear fitting problem, especially for a large number of noisy peaks typical for mass spectrometry. Noisy data impedes the construction of a list of peaks or spectral lines from the harmonic transient using these alternatives to Fourier Transforms. Alternative methods to obtain data, to analyse data or both using FTMS are desirable to reduce detection time without degradation in resolving power.